Zatcoff Factoring When A Does Not = 1

1) Factor

7 x squared minus 16 x plus 4

(x - 3)(7x + 5)

(x - 4)(7x + 1)

(x + 2)(7x - 4)

(x - 2)(7x - 2)

The given expression can be factored as (x - 2)(7x - 2). This can be determined by using the distributive property to multiply the two binomials together. The first terms in each binomial, x and x, multiply to give x^2. The outer terms, x and -2, multiply to give -2x. The inner terms, -2 and 7x, multiply to give -14x. And the last terms, -2 and -2, multiply to give 4. Combining like terms, we have x^2 - 2x - 14x + 4, which simplifies to x^2 - 16x + 4. Therefore, the correct factorization is (x - 2)(7x - 2).

Explanation

The given expression can be factored as (x - 2)(7x - 2). This can be determined by using the distributive property to multiply the two binomials together. The first terms in each binomial, x and x, multiply to give x^2. The outer terms, x and -2, multiply to give -2x. The inner terms, -2 and 7x, multiply to give -14x. And the last terms, -2 and -2, multiply to give 4. Combining like terms, we have x^2 - 2x - 14x + 4, which simplifies to x^2 - 16x + 4. Therefore, the correct factorization is (x - 2)(7x - 2).

2) Factor:

15 z squared plus 2 z minus 8

(3z+2)(5z-4)

(3z-2)(5z+4)

(15z-2)(z+4)

(15z - 2)(z - 8)

The given expression is a product of two binomials. To determine the correct answer, we need to use the distributive property to multiply the terms in each binomial. When we apply the distributive property to (3z+2)(5z-4), we get 15z^2 - 12z + 10z - 8. Simplifying further, we have 15z^2 - 2z - 8. This matches the expression in the answer choice (3z-2)(5z+4), so it is the correct answer.

Explanation

The given expression is a product of two binomials. To determine the correct answer, we need to use the distributive property to multiply the terms in each binomial. When we apply the distributive property to (3z+2)(5z-4), we get 15z^2 - 12z + 10z - 8. Simplifying further, we have 15z^2 - 2z - 8. This matches the expression in the answer choice (3z-2)(5z+4), so it is the correct answer.

3) Factor:

2 x squared minus 12 x plus 16

2(x - 8)(x + 1)

(x - 2)(2x - 8)

2(x - 2)(x - 4)

(x - 2)(x - 4)

The correct answer is 2(x - 2)(x - 4). This is because when we multiply out the factors, we get 2(x^2 - 6x + 8), which simplifies to 2x^2 - 12x + 16. This matches the given expression, so it is the correct answer.

Explanation

The correct answer is 2(x - 2)(x - 4). This is because when we multiply out the factors, we get 2(x^2 - 6x + 8), which simplifies to 2x^2 - 12x + 16. This matches the given expression, so it is the correct answer.

4) Which binomial is a factor of

6 x squared plus x minus 12 ?

3x - 3

3x - 4

6x + 3

X + 4

The binomial 3x - 4 is a factor of the given expression because when we divide the expression by 3x - 4, we get a quotient without any remainder. This means that 3x - 4 divides evenly into the expression, and therefore it is a factor.

Explanation

The binomial 3x - 4 is a factor of the given expression because when we divide the expression by 3x - 4, we get a quotient without any remainder. This means that 3x - 4 divides evenly into the expression, and therefore it is a factor.

5) Factor completely:

10 x squared minus space 35 x space minus space 20

(2x - 1)(5x+20)

5(2x - 1)(x + 4)

5(2x + 1)(x - 4)

(2x + 1)(x + 4)

The given expression can be factored completely as 5(2x + 1)(x - 4). This is obtained by applying the distributive property to the expression 5(2x - 1)(x + 4). The common factor of 5 can be pulled out, and the remaining expressions inside the parentheses can be multiplied together.

Explanation

The given expression can be factored completely as 5(2x + 1)(x - 4). This is obtained by applying the distributive property to the expression 5(2x - 1)(x + 4). The common factor of 5 can be pulled out, and the remaining expressions inside the parentheses can be multiplied together.